In order to find the optimum index profile of the single-mode optical fiber with respect to the cabling loss due to the random bends with the Gaussian correlation function, the relation between the random-bend loss and the index profile is investigated. The formula of the random-bend loss is derived for arbitrary index profile. In the derivation, the loss is calculated as the power of dipole radiation due to the equivalent refractive index perturbation in contrast with the conventional mode coupling analysis. Using this formula, random-bend losses are calculated for four types of index profiles; the convex, parabolic, step, and concave type of index profiles, under the condition that connection losses are same for all types of profiles. As results of the comparison, the random-bend loss is minimum in the case of the convex type of profile and it is decreased down to 40% of that in the case of the step profile.